In preferred embodiments, a cryptographic device in which two key sets are stored: a normal key set (typically unique to the device) and a test key set (typically used by each of a relatively large number of devices). The device uses the normal key set in a normal operating mode and uses the test key set in at least one test mode which can be a built-in self test mode. Alternatively, the device stores test data (e.g., an intermediate result of an authentication exchange) in addition to or instead of the test key set. In other embodiments, the invention is a cryptographic device including a cache memory which caches a portion of a key set for performing an authentication exchange and/or at least one authentication value generated during an authentication exchange. Other embodiments of the invention are systems including devices that embody the invention and methods that can be performed by systems or devices that embody the invention.